She wasn't permitted to look at the "Apollo Belvedere" while photographers were around. But Nancy Reagan managed to see the world-famous Roman marble statue in "polite society" tonight at the opening of "The Vatican Collections--The Papacy and Art" at the Metropolitan Museum of Art.

"She adored it," said Mrs. Charles W. Englehard, who with Brooke Astor was cochairman of the Committee of Welcome for the priceless collection of the paintings, sculpture, tapestries and other works of art the public will be allowed to view starting Feb. 26.

Mrs. Reagan, as honorary chairman of the committee, joined Cardinal Terence Cooke here for the gala preview and dinner of the first major art exhibition sent abroad from the Vatican.

Wearing a black-beaded gown by Galanos, the first lady posed for pictures with Cooke, Philippe de Montebello, director of the Metropolitan, C. Douglas Dillon, member of the Metropolitan Board of Directors, and George Weissman, chairman of the board and chief executive officer of Phillip Morris, which paid $3 million to bring the 237 works from Rome to New York.

Mrs. Reagan said, "I will leave tomorrow with the memory of all this beauty forever in my heart." She said she would have to "go back three or four times to see everything."

The first lady's route through the exhibition had been carefully advanced, and according to a Metropolitan official the stunning "Apollo Belvedere" had been eliminated from her public inspection.

"It's undressed, for one thing," said one museum official. "For another, it's on a quite high pedestal and not good for pictures. The 'Apollo Belvedere' is by far the most famous of the statues, but this is what the White House wanted and we do it their way."

The guests were a bejeweled crowd of art patrons, collectors and social luminaries who dallied through the exhibition virtually in awe of what they were seeing.

Coming from Rome for the occasion was the U.S. envoy to the Vatican and close personal friends of the Reagans, William Wilson and his wife, Betty. They toured with other close Reagan friends, millionaire-publisher Walter Annenberg and his wife, Lee, the former U.S. chief of protocol.

"My favorite is the 'Apollo Belvedere' and the 'Apollo Torso,' " said art collector Annenberg. "When you look at the 'Belvedere' torso you can see that Michelangelo studied that endlessly because it appears in all his work--at least that's the way I interpret it."

Wilson said it was "just marvelous that the people of the United States can see a small portion of the huge amount of art that is available in the Vatican. The fact that they were willing to send it over is significant in the relationship between the United States and the Vatican."

J. Carter Brown, director of the National Gallery of Art, and his wife, Pamela, were in the throng, dining in the dramatic Temple of Dendur, where a pool reflected the sparkling lights of the party. When De Montebello saw Brown he told him that "the thing I'm the most jealous of is the Watteau exhibit. In many ways he's the greatest painter who ever lived. I would take that any time. When is that coming? '84? To die," De Montebello said while Carter Brown listened with a fixed smile.

Asked about a report that the new Vatican exhibit had sparked a controversy in Italy and that the Italian government had put a moratorium on sending future exhibits abroad, De Montebello poo-pooed the story.

"There may be a few conservatives talking in the press, but there is no moratorium," said De Montebello, whose idea it had been to bring an exhibit of Vatican treasures to the Metropolitan.

Did he think the National Gallery in Washington might be somewhat jealous of his coup?

"You have to ask them," he said, turning and walking off.

Among the guests were people like former New York City mayor Robert Wagner, who later became America's envoy to the Vatican.

"A couple of fellows waved at me though they were a little old," Wagner quipped of some of the antiquities he had seen when he lived in Rome.

Others in the crowd included Albert Grimaldi, better known as Prince Albert of Monaco; two former secretaries of state, Henry Kissinger and William Rogers; the first lady of Uruguay, Rosario Flores de Alverez, whom Cardinal Cooke had personally invited to last night's opening; Douglas Fairbanks Jr.; Mary Lasker; Ron Reagan and his wife, Doria; and Helen Boehm who stood transfixed when she saw "Apollo Belvedere."

"I'm in love--I'm in love," she said to all around her.